Odpowiedź:
Poziom D
a) x^2 + 3 = 4 • x x = 1
L = x^2 + 3 = 1^2 + 3 = 1 • 1 + 3 = 1 + 3 = 4
P = 4 • x = 4 • 1 = 4
L = P
x^2 + 3 = 4 • x x = 2
L = x^2 + 3 = 2^2 + 3 = 2 • 2 + 3 = 4 + 3 = 7
P = 4 • x = 4 • 2 = 8
L =/ P
x^2 + 3 = 4 • x x = 3
L = x^2 + 3 = 3^2 + 3 = 3 • 3 + 3 = 9 + 3 = 12
P = 4 • x = 4 • 3 = 12
L = P
Odp. : Rozwiązaniem tego równania są liczby 1 i 3.
b) x^2 - 1 = 8 x = 1
L = x^2 - 1 = 1^2 - 1 = 1 • 1 - 1 = 1 - 1 = 0
P = 8
L =/ P
x^2 - 1 = 8 x = 2
L = x^2 - 1 = 2^2 - 1 = 2 • 2 - 1 = 4 - 1 = 3
P = 8
L =/ P
x^2 - 1 = 8 x = 3
L = x^2 - 1 = 3^2 - 1 = 3 • 3 - 1 = 9 - 1 = 8
P = 8
L = P
Odp. : Rozwiązaniem tego równania jest liczba 3.
c) (x - 1) • (x - 1) = x^2 - 1 x = 1
L = (x - 1) • (x - 1) = (1 - 1) • (1 - 1) = 0
P = x^2 - 1 = 1^2 - 2 = 1 • 1 - 1 = 0
L = P
(x - 1) • (x - 1) = x^2 - 1 x = 2
L = (x - 1) • (× - 1) = (2 - 1) • (2 - 1) = 1 • 1 = 1
P = x^2 - 1 = 2^2 - 1 = 2 • 2 - 1 = 4 - 1 = 3
L =/ P
(x - 1) • (x - 1) = x^2 - 1 x = 3
L = (x - 1) • (x - 1) = (3 - 1) • (3 - 1) = 2 • 2 = 4
P = x^2 - 1 = 3^2 - 1 = 3 • 3 - 1 = 9 - 1 = 8
L =/ P
Odp. : Rozwiązaniem tego równania jest liczba 1.
d) 12/x+1 = x + 2 x = 1
L = 12/x+1 = 12/1+1 = 12/2 = 6
P = x + 2 = 1 + 3 = 4
L =/ P
12/x+1 = x + 2 x = 2
L = 12/x+1 = 12/2+1 = 12/3 = 4
P = x + 2 = 2 + 2 = 4
L = P
12/x+1 = x + 2 x = 3
L = 12/x+1 = 12/3+1 = 12/4 = 3
P = x + 2 = 3 + 2 = 5
L =/P
Odp. : Rozwiązaniem tego równania jest liczba 2.
e) (x - 1) • (x - 3) • (x - 2) = x - x x = 1
L = (x - 1) • (x - 3) • (x - 2) = (1 - 1) • (1 - 3) • (1 - 2) =
= 0 • (-2) • (-1) = 0
P = x - x = 1 - 1 = 0
L = P
(x - 1) • (x - 3) • (x - 2) = x - x x = 2
L = (x - 1) • (x - 3) • (x - 2) = (2 - 1) • (2 - 3) • (2 - 2) =
= 1 • (-1) • 0 = 0
P = x - x = 2 - 2 = 0
L = P
(x - 1) • (x - 3) • (x - 2) = x - x x = 3
L = (x - 1) • (x - 3) • (x - 2) = (3 - 1) • (3 - 3) • (3 - 2) =
= 2 • 0 • 1 = 0
P = x - x = 3 - 3 = 0
L = P
Odp. : Rozwiązaniem tego równania są liczby 1, 2 oraz 3.
f) (x + 6) : 2 = x • 2 x = 1
L = (x + 6) : 2 = (1 + 6) : 2 = 7 : 2 = 3,5
P = x • 2 = 1 • 2 = 3
L =/ P
(x + 6) : 2 = x • 2 x = 2
L = (x + 6) : 2 = (2 + 6) : 2 = 8 : 2 = 4
P = x • 2 = 2 • 2 = 4
L = P
(x + 6) : 2 = x • 2 x = 3
L = (x + 6) : 2 = (3 + 6) : 2 = 9 : 2 = 4,5
P = x • 2 = 3 • 2 = 6
L =/ P
Odp. : Rozwiązaniem tego równania jest liczba 2.
Szczegółowe wyjaśnienie:
Jakby co to L =/ P to jest lewa nie równa się prawej
Pozdrawiam.
